Nitrogen and potassium application effects on productivity, profitability and nutrient use efficiency of irrigated wheat (Triticum aestivum L.)

The development of robust nutrient management strategies have played a crucial role in improving crop productivity, profitability and nutrient use efficiency. Therefore, the implementation of efficient nutrient management stratigies is important for food security and environmental safety. Amongst the essential plant nutrients, managing nitrogen (N) and potassium (K) in wheat (Triticum aestivum L.) based production systems is citically important to maximize profitable production with minimal negative environmental impacts. We investigated the effects of different fertilizer-N (viz. 0–240 kg N ha-1; N0-N240) and fertilizer-K (viz. 0–90 kg K ha-1; K0-K90) application rates on wheat productivity, nutrient (N and K) use efficiency viz. partial factor productivity (PFPN/K), agronomic efficiency (AEN/K), physiological efficiency (PEN/K), reciprocal internal use efficiency (RIUEN/K), and profitability in terms of benefit-cost (B-C) ratio, gross returns above fertilizer cost (GRAFC) and the returns on investment (ROI) on fertilizer application. These results revealed that wheat productivity, plant growth and yield attributes, nutrients uptake and use efficiency increased significantly (p<0.05)with fertilizer-N application, although the interaction effect of N x K application was statistically non-significant (p<0.05). Fertilizer-N application at 120 kg N ha-1 (N120) increased the number of effective tillers (8.7%), grain yield (17.3%), straw yield (15.1%), total N uptake (25.1%) and total K uptake (16.1%) than the N80. Fertilizer-N application significantly increased the SPAD reading by ~4.2–10.6% with fertilizer-N application (N80-N240), compared with N0. The PFPN and PFPK increased significantly with fertilizer-N and K application in wheat. The AEN varied between 12.3 and 22.2 kg kg-1 with significantly higher value of 20.8 kg kg-1 in N120. Fertilizer-N application at higher rate (N160) significantly decreased the AEN by ~16.3% over N120. The N120treatment increased the AEK by ~52.6% than N80 treatment. Similarly the RIUEN varied between 10.6 and 25.6 kg Mg-1 grain yield, and increased significantly by ~80.2% with N120 as compared to N0 treatment. The RIUEK varied between 109 and 15.1 kg Mg-1 grain yield, and was significantly higher in N120 treatment. The significant increase in mean gross returns (MGRs) by ~17.3% and mean net returns (MNRs) by ~24.1% increased the B-C ratio by ~15.1% with N120 than the N80 treatment. Fertilizer-N application in N120 treatment increased the economic efficiency of wheat by ~24.1% and GRAFC by ~16.9%. Grain yield was significantly correlated with total N uptake (r = 0.932**, p<0.01), K uptake (r = 0.851**), SPAD value (r = 0.945**), green seeker reading (r = 0.956**), and the RIUEN (r = 0.910**). The artificial neural networks (ANNs) showed highly satisfactory performance in training and simulation of testing data-set on wheat grain yield. The calculated mean absolute error (MAE), mean absolute percentage error (MAPE) and root mean square error (RMSE) for wheat were 0.0087, 0.834 and 0.052, respectively. The well trained ANNs model was capable of producing consistency for the training and testing correlation (R2 = 0.994**, p<0.01) between the predicted and actual values of wheat grain yield, which implies that ANN model succeeded in wheat grain yield prediction.


Introduction
Wheat (Triticum aestivum L.) is extensively utilized in human consumption and has high rank globally among the most essential cereals grown worldwide. It accounts for~30% of all cereal food worldwide and staple food for~10 billion people in~43 countries of the world [1,2]. The most important factors influencing the wheat grain quality parameters are the environment, genotype and the potential interactions among these factors [3,4]. Nitrogen is most important yield limiting nutrients for crop growth in different agro-ecological regions. Fertilizer-N affect the physiological (i.e. respiration rate, water balance, signaling pathways) [5] and metabolic (i.e. enzyme activity, photosynthesis rate) processes of plants, which influencing plant growth [6,7]. Research on N fertilization to cereal crops has been well highlighted because of its essential role in high yielding systems [8][9][10], improved dough quality and the potential for environmental impacts due to low N use efficiency [10,11].
After N, potassium (K) is absorbed in large amount than any other element [12] and plays a lead role in increasing crop yield and improving the product quality [13,14]. Potassium supply is considered as a limiting factor, given its high accumulation in cereals [15,16]. Fertilizer-K application is required for plant survival, carbohydrate and proteins syntheses, cell evolution which helps in maintaining the ionic cell balance and acts as an enzyme activator besides activating the photosynthetic enzymes, assimilates translocation [17,18] and enhance stress tolerance [19,20]. Potassium effectively coordinates the relationship between source and sink of starch synthesis and transport and transformation of photosynthates [21]. But, imbalanced fertilizer application in crop production has become common in many developing countries [10,22,23]. The practice often leads to an excess of fertilizer-N application with a serious environmental implications [24], besides continual depletion of soil K mainly due to inadequate K supply [22]. Over application of fertilizer-N leads to enrichment of reactive N constituents, transformation of soil N forms and also affects soil acidification, with resultant impairment of ecosystems [24,25]. Bijay-Singh et al. [26] reported that to a large percentage of area under rice-wheat system, very little or no fertilizer-K is being applied and therefore, most of it comes from K-reserves of the soil. There are many causes of low K use in farmers' fields, such as the effect of K in vegetative crop growth is not very clear, K fertilizer are more costly than fertilizer-N, and sometimes it is not available in the local market [27].
The apparent recovery of nutrients from applied fertilizers for cereal crops is typically low [28,29]. Recent evidence suggests that the co-application of fertilizers (P, K and S) can improve the recovery of fertilizer-N and increased N efficiency [30]. The causes of yield gaps due to nutrient deficiencies and imbalances among regions can be enhanced yields~20-30%, by management practices [31]. Therefore, a better characterization of wheat response to fertilizer application and interactions among nutrients is essential for sustainable improvements in yield [32]. While extensive research has explored the wheat response to fertilizer-N, P, and K over the years, but with few exceptions [33,34] most studies were usually limited in geography [35,36] or on temporal scale [36,37]. Fertilizer-N application intensifies K requirement of crops due to yield gain benefits, therefore, high K application rates become essential to achieve higher crop yields [38]. Contrarily, increasing fertilizer-N application to crops with insufficient soil K status could increase K recycling from the deep layers. Therefore, the fertilizer-N and K application rates must be adjusted to optimize and rationalize crop demand and reduce the negative impacts on soils' K reserves due to high K mining [39].
While extensive research has explored wheat crop response to fertilizer-N, P, and K over the years [36, 37] but provided a limited potential to extrapolate the interactive effect of N and K on wheat yield and nutrient use efficiency. Additionally, despite potential interaction effects of fertilizer rates (N, P, and K) on crop's responses [38], most studies focused on one nutrients at a time [30,39], and very few studies attempted to explore the interaction effects among fertilizer-N, and K applications [33]. Wheat yield response to fertilizer-K depends on the N nutrition level and the interaction is usually positive [40]. Nonetheless, fertilizer-K application facilitates the absorption and transport of nitrate-N (NO 3-N) to the shoots of the plant and transports it later on to the aerial plant parts, which in turn increases the activities of N [41,42]. The availability and proper ratio in the soil are important factors for plant growth and development [38]. In addition, changes in NH 4 + /NO 3 − ratios and K supply levels influence the yield and nutrient uptake of wheat [43]. Therefore, interaction effect of fertilizer-N and K can be assessed by with wide range of fertilizer application rates of two or more nutrients on nutrient uptake, yield and nutrient use efficiency. A better understanding of fertilizer-N and -K interactions affecting crop yield and nutrient use efficiency has important agronomic consequences in economic and environmental context. Therefore, the objective of this field experiment was to investigate fertilizer-N by K interaction in wheat by evaluating the effects of wide range of fertilizer-N and K applications in different combinations on yield, nutrient use efficiency and economic indices in irrigated sandy loam ellitic soil in north-western India.

Yield attributes and crop productivity
Fertilizer-N application significantly (p<0.05) increased the number of effective tillers and non-effective tillers during 2 study years, while fertilizer-K application did not increased the number of effective tillers of wheat (Table 1). Data pooled for study years showed that N 160 increased the number of effective tillers by~3.4-times, compared with the N 0 . Similarly, N 160 increased the number of non-effective tillers significantly over the N 0 . At higher fertilizer-N applications, the number of effective and non-effective tillers did not increased significantly. The plant height and spike length did not increased significantly with fertilizer-N and K application. The root dry weight increased significantly by 25.6 g plant -1 (~164%) with N 120 compared with N 0 . The interaction effect of fertilizer-N and K application on yield attributes of wheat was statistically non-significant. Fertilizer-N application increased the root dry weight up to fertilizer-N application rate of 120 kg N ha -1 , and thereafter there was no change in the root dry weight (Fig 1). The relationship between fertilizer-N application rates and root dry weight of wheat could best be expressed as Eq 1.
Root dry weight ðg plant À 1 Þ Wheat grain yield increased significantly up to N 120 during 2014, while in 2013 the significant increase was observed up to N 160 (Table 2). Data pooled for two years showed that wheat grain yield was increased by 2.5 Mg ha -1 (~76.5%) with N 120 , compared with N 0 . Similarly, straw yield did not increased significantly with N 160 than the N 120 . The fertilizer-N and K application did not significantly increase the harvest index of wheat. The interaction effect of fertilizer-N and K on wheat grain and the harvest index was non-significant. Fertilizer-K application at K 90 resulted in significant increase in wheat straw yield. Fig 2 illustrates that wheat grain yield increased in non-linear way with fertilizer-N application, and the relationship between fertilizer-N application rates and wheat grain yield could best be described by Eq 2.

Nutrient uptake and leaf greenness
Fertilizer-N application significantly increased the grain, straw and total (grain + straw) N uptake by wheat during the study years (Table 3). Grain N uptake increased significantly with N 160 compared with N 120 during the second years, but non-significantly during the first year. Data pooled for two study years revealed that grain N uptake was significantly increased with N 160 than the N 120 . Grain-N uptake was increased by~3.5 and 4.0-times with N 120 and N 160 , respectively over the N 0 . As compared with N 120 , N 160 resulted in~15.5% increase in grain N uptake by wheat. The highest straw N uptake was observed with N 240 ; although N 120 and N 160 increased the straw N uptake by~2.8 and 3.1-times than the N 0 . The total N uptake by wheat varied between 33.3 and 158.4 kg ha -1 ; showing an increase of~3.8 and 4.0-times with N 120 and N 160 over N 0 . These results revealed that increased fertilizer-N rate of N 160 resulted in only~6.7% increase in total N uptake by wheat. It was important to note that fertilizer-K application did not result in significant change in total N uptake by wheat. The interaction effect of fertilizer-N and K application was statistically non-significant.
Fertilizer-N application significantly increased the SPAD reading by~4.2-10.6% with fertilizer-N application (N 80 -N 240 ), compared with N 0 (Fig 3). At higher fertilizer-N rate (N 160 ) the SPAD reading increased by~2.3%, compared with N 120 . Fertilizer-K application did not significantly change the SPAD reading. The green seeker value followed the similar trend to that of the SPAD reading, with no significant change due to fertilizer-K application. Fig 4 illustrates the relationship between SPAD value and grain, straw and total N uptake by wheat. The relationship indicates increase in N uptake with the increase in SPAD value, which could best be described by  Grain N uptake ðkg N ha À 1 Þ ¼ À 2:526 ðSPAD readingÞ 2 þ 217:0 ðSPAD readingÞ À 4540; R 2 ¼ 0:971 ð3Þ Straw N uptake ðkg N ha À 1 Þ ¼ À 0:36 ðSPAD readingÞ 2 þ 32:98 ðSPAD readingÞ À 716:9; Total N uptake ðkg N ha À 1 Þ ¼ À 2:888 ðSPAD readingÞ 2 þ 250:1 ðSPAD readingÞ À 5259; R 2 ¼ 0:969 ð5Þ Fig 5 showed the green seeker value in response to fertilizer-N application in wheat. The N uptake exhibited an increase as a function of green seeker reading (Fig 6). The relationship between green seeker reading and N uptake by straw, grains and total N uptake has been

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Nitrogen and potassium application effects on wheat (Triticum aestivum L.)

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Nitrogen and potassium application effects on wheat (Triticum aestivum L.) expressed in Eqs 6-8.
Grain N uptake ðkg N ha À 1 Þ ¼ 153:6 ðgreen seeker readingÞ 6:377 ; Straw N uptake ðkg N ha À 1 Þ ¼ 0:876 ðgreen seeker readingÞ 5:542 ; Total N uptake ðkg N ha À 1 Þ ¼ 191:7 ðgreen seeker readingÞ 6:188 ; Fertilizer-N application resulted in a significant increase in K uptake by grains and straw ( Table 4). Data pooled for two years showed that grain K uptake varied between 11.8 and 22.3 kg ha -1 ; with~84.7% increase in N 120 than the N 0 treatment. There was non-significant difference in grain K uptake at higher fertilizer-N rates (N 160 -N 240 ). These results showed that wheat straw K uptake was significantly increased with N 120 ; followed by non-significant change at higher fertilizer-N rates. The total K uptake followed the similar response to fertilizer-N application, with highest K uptake at N 120 . Data pooled for different study shows that there was non-significant difference in grain, straw and total K uptake with different rates of fertilizer-K application. Nonetheless, the interaction effect of fertilizer-N and K on K uptake by grains and straw was non-significant.

Nitrogen and potassium use efficiency
The PFP N decreased significantly with increased fertilizer-N application rate in wheat, but do not differ significantly with the application of fertilizer-K (Table 5). Data pooled for different study years showed that PFP N for wheat varied between 25.9 and 61.5 kg ha -1 ; with the highest in N 80 and the lowest in N 240 . The N 160 treatment decreased the PFP N by 10.1 kg ha -1 (~21.0%), compared with N 120 . The AE N varied between 12.3 and 22.2 kg kg -1 with significantly higher value of 20.8 kg kg -1 in N 120 . Fertilizer-N application at higher rate (N 160 ) significantly decreased the AE N by~16.3% over N 120 . The two year pooled data showed that PE N was significantly higher with N 120 by~44.6% than the N 240 . It was important to observe that PE N Table 4. Effect of nitrogen (N) and potassium (K) application on K uptake by grain and straw of wheat (Triticum aestivum L.) in a sandy loam soil in sub-tropical India.

Treatment
Grain K uptake (kg ha -1 ) Straw K uptake (kg ha -1 ) Total K uptake (kg ha -1 ) did not differ significantly among N 120 and N 160 . The RIUE N varied between 10.6 and 25.6 kg Mg -1 grain yield, and increased significantly by~80.2% with N 120 as compared to N 0 treatment. The RIUE N did not differ significantly among N 120 and N 160 . The effect of fertilizer-K and interaction effect of fertilizer-N and K was statistically non-significant for PFP N , AE N , PE N and the RIUE N . The PFP K increased significantly with fertilizer-N and K application in wheat (Table 6). Fertilizer-N application at 120 kg N ha -1 increased the PFP K by 38.3 kg ha -1 (~76.9%), compared with the N 0 treatment. However, the PFP K did not differ significantly among different fertilizer-N application rates (N 80 -N 240 ). The PFP K was highest at K 30 and decreased bỹ 2-times with K 60 treatment. Fertilizer-N application at N 120 increased the AE K by~52.6% Table 5. Main plot (N application) than N 80 treatment. Similarly, K 30 treatment had the highest, while the K 90 had the significantly lower AE K . The PE K was highest in N 160 , which was~19.8% higher than N 120 treatment. The PE K did not differ significantly with fertilizer-K application at different rates. The RIUE K varied between 109 and 15.1 kg Mg -1 grain yield, and was significantly higher in N 120 treatment. The effect of fertilizer-K and interaction effect of fertilizer-N and K on RIUE K of wheat crop statistically non-significant.

Available nitrogen and potassium content
Fig 7 showed that available-N content in soil was significantly increased with fertilizer-N application. The available-N content in soil increased by~37.3% with N 120 treatment compared with the N 0 . There was non-significant change in available-N content in soil with fertilizer-N application rates of N 120 , N 160 , N 200 and N 240 . Fertilizer-K application had non-significant effect on available-N content in soil. Available-K content in soil was highest in N 120 treatment, and was~8.3% higher than N 0 (Fig 8). Fertilizer-K application at K 30 , K 60 and K 90 increased the available-K content in soil by~9.1, 11.5 and 15.3%, respectively.

Economic analysis
The MCCIs varied between 364 US$ ha -1 and 408 US$ ha -1 yielded MGRs of 835 US$ ha -1 and 1594 US$ ha -1 for different fertilizer-N and K application treatments in wheat ( Table 7). The MGRs were significantly higher by~17.3% with N 120 as compared to N 80 . The application of higher fertilizer-N application rates did not significantly increased the MGRs for wheat cultivation. The MNRs varied between 471 US$ ha -1 for N 0 and 1187 US$ ha -1 for N 240 treatments. Similarly, the MNRs varied between 1115 and 1130 US$ ha -1 among different fertilizer-K treatments (K 0 -K 90 ). Fertilizer-N application at 120 kg N ha -1 (N 120 ) resulted in significantly higher MNRs by~24.1% than the N 80 treatment. The B-C ratio was significantly increased by~66.1% with N 120 than the N 0 treatment. The higher fertilizer-N application rates (N 160 -N 240 ) resulted in~1.4-3.4% increase in B-C ratio of wheat. The economic efficiency of wheat increase bỹ 24.1% with N 120 than N 80 treatments; however, the higher fertilizer-N application rates did not significantly increase the economic efficiency. The GRAFC varied between 835 and 1550 US$ ha -1 ; a significantly higher returns (by~210 US$ ha -1 ;~16.9%) were obtained under N 120 than N 80 . The ROI of 66.9 US$ gross returns US$ -1 cost were significantly higher by~84.8% in N 120 than the N 240 treatment. At lower fertilizer-N application rate (N 80 ), the ROI although increased by~23.3%, but were statistically non-significant.

Evaluation of ANN developed for predicting wheat grain yield
A back propagation neural network with Levenberg Marquardt algorithm was used to establish the relationship between the input variables viz. grain N uptake, straw N uptake, grain K uptake, straw K uptake, total N uptake, total K uptake, SPAD value, green seeker value, RIUE N and RIUE K and the wheat grain yield. We applied back propagation neural networks technique, self-organizing map (SOM) neighbour weight distance and ANNs consisted of several layers of neurons which are inter-connected and then the weights were assigned to those interconnections (Fig 9). The SOM is an unsupervised machine learning use to produce a lowdimensional representation of a higher dimensional data-set while preserving the topological structure of the data. The SOM depicts the input data as a table with a row for each value of input variable, and columns for each variable containing each value. The SOM algorithm arranged these variables in a two-dimensional grid placing with similar variable closer together. The schematic representation of weights (weight-1 and weight-2) assigned to the inter-connections for inputs used for the simulation of wheat grain yield has been shown in Fig 10. The ANNs exhibit a highly satisfactory performance in training and simulation of testing data-set, which indicates that a well-trained ANN model is well capable of producing consistent and accurate results. This consistency between the training and testing has been clearly illustrated in Fig 11. A high correlation (R 2 = 0.994 �� , p<0.01) between the predicted and actual values of wheat grain yield, which implies that ANN model succeeded in wheat grain yield prediction. Table 9 shows test statistics for ANN model evaluation (Fig 12). The calculated MAE, MAPE and RMSE for wheat were 0.0087, 0.834 and 0.052, respectively. The lowest possible RMSE value is zero, indicating that there is no difference between the actual and predicted data.

Discussion
The fertilizer-N application significantly (p<0.05) increased the number of effective and noneffective tillers during 2 study years, while fertilizer-K application did not increased the yield  -1 and weight-2) assigned to the inter-connections for inputs used for the simulation of wheat grain yield using ten different input layers viz. grain N uptake, straw N uptake, grain K uptake, straw K uptake, total N uptake, total K uptake, SPAD value, green seeker value, RIUE N and RIUE K . https://doi.org/10.1371/journal.pone.0264210.g011

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Nitrogen and potassium application effects on wheat (Triticum aestivum L.) attributing characters of wheat. The total number of tillers increased as a function of N application rates across all levels of K rate, but peaked up at 120 kg N ha -1 . This could be major contribution of N towards cell division, elongation and enhancing the vegetative growth, and K contribute in promoting vigorous plant growth through efficient photosynthesis [44]. The individual application effect of fertilizer-N and K on number of tillers of wheat have been reported earlier [45,46]. Furthermore, Bundy and Andraski [47] reported the combined application of fertilizer-N and K on increased tiller production. The number of effective tillers facilitates the identification of the number of spikes that plant generates, as they can survive and Table 9.

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Nitrogen and potassium application effects on wheat (Triticum aestivum L.) produce grains [48]. The requirement for high wheat yields was influenced by population growth and development, mainly in terms of the increased tiller number per unit area [49]. The application of fertilizer-K was observed to regulate the N metabolism, which increases its absorption by the plant [50]. Therefore, when fertilizer-N and K are applied together, they enhance vegetative growth and resulted in increased number of fertile tillers per unit area.
Fertilizer-N fluxes in agro-ecosystems are important for assessing the effectiveness for wheat yield and in determining probable environmental contamination [51, 52]. The optimal fertilizer-N plays a positive role in the crop growth and productivity and helps improve the profitability and nutrient use efficiency. Some studies have shown that fertilizer-N application could increase crop yield, whereas excessive fertilizer-N aplication lead to yield reduction. In the present study, wheat grain yield increased significantly up to N 120 , compared with higher level of fertilizer-N application rates, while K application did not significantly increase the wheat grain yield. In case of control, the growth and development of plants were hampered due to imbalance uptake of essential elements, which resulted in poor performance of yield attributes and ultimately gave the lowest wheat grain yield. These findings suggested that when the rate of fertilizer-N application increased to a certain extent (N 160 -N 240 ), the wheat yield would not significantly increase, but there was no-significant decline. Therefore, similar to previous research [53], these results also shows that higher fertilizer-N application rates ensured higher crop yield, but was not necessary to achieve significant yield gain advantage. Similar to the grain yield, fertilizer-N application rate significantly increased crop N accumulation compared with the N 0 control. However, the amount of N absorbed by crops on crop yield is affected by genetic and environmental factors, compromising the relationship between fertilizer-N application rate and its accumulation in the crop [54]. Unfortunately, most farmers applied the amount of fertilizer-N based on their experience, rather than testing soil nutrients and plant growth [55]. This strongly suggests that fertilizer-N rate above 120 kg N ha -1 , the N utilization by plants were nearly negligible and exposed to leaching, volatilization and immobilization losses. These results illustrates that combination of 120 kg N ha -1 with 30 kg K ha -1 increased the ability of plants for capturing resources and increased dry matter accumulation. In the present study, the effect of higher dose of fertilizer-K application (K 60-90 ) or the interaction effect of fertilizer-N and K was statistically non-significant (p<0.05). The soils of studied region in north-western India are mostly containing smectite and illitic clay minerals [56]. When K is removed by plant roots from the soil solution, more K is released from the clay minerals by cation exchange. Nonetheless, average amount of K contributed to wheat through irrigation with underground water varied from 8 kg in piedmont plain to 28 kg ha -l each in alluvial plain with occasional sand dune and alluvial plain with sand dune, respectively [57].

Nutrient uptake and leaf greenness
Fertilizer-N application significantly increased the grain, straw and total N uptake by wheat during the study years up to 120 kg N ha -1 as compared to higher rates of fertilizer-N application. Different rates of fertilizer-K application was showed non-significant difference in grain, straw and total K uptake. When the fertilizer-N application rate exceeds crop demand, the quantity of applied fertilizer-N used by the crops is reduced, and a larger amount of applied N remains in the soil or is lost [58]. In contrast, when the fertilizer-N rate is less than crop demand, soil N is depleted [59]. Therefore, the accumulation and loss of NO 3 -N in soil could be reduced by applying less amounts of fertilizer-N than or equal to that required for the optimal crop yield [25,60].
The chlorophyll fluorescence parameters were used to estimate the function of photosynthetic apparatus and carbon assimilation rate due to its sensitivity, accessibility and non-intrusive features [61,62]. The leaf N content has been linked directly to the chlorophyll index [63], and varied with each phenological stage [64]. The reduction in light intensity and alterations in light spectrum under fertilizer-N application rates has shown to alter chloroplast ultra-structure and chlorophyll contents [61,65]. In this study, fertilizer-N application significantly increased the SPAD value and green seeker reading by~4.2-10.6% and 0.89-0.97%, respectively with fertilizer-N application (N 80 -N 240 ), compared with N 0 . Viana and Kiehl [38] reported that the chlorophyll index increased with fertilizer-N and potassium application. Teixeira Filho et al. [66] assessed the chlorophyll concentration in wheat plants and also reported that the fertilizer-N application rates influenced the leaf chlorophyll index, with maximum valued achieved was 46 N corresponding to the applied N dose of 147 kg N ha -1 .

Nitrogen and potassium use efficiency
Nitrogen use efficiency is represented with N recovered efficiency in the crops and has a significant impact on air and water quality, biodiversity, and human health [67,68]. The higher nutrient use efficiency is generally reflected to be the adaptation of crops to a habitat with low soil N supply [69]. In the present study, fertilizer-N application at higher rate (N 160 -N 240 ) significantly decreased the N use efficiencies over N 120. However, the K use efficiency did not differ significantly among different fertilizer-K application rates. These results corroborate earlier research findings of highest N use efficiency at the lower rate because of less losses [70,71]. At the lower rate of fertilizer-N, the wheat plant mostly utilized the supplied N for grain yield. Hagos et al. [72] and Mesele [73] reported that that K use efficiency decreased when the rate of fertilizer-K application increases. The higher nutrient use efficiency was recorded at lower rates of fertilizer-N and K application in the present study. As reported by Bijay-Singh [74], if a unit of fertilizer to pay for its cost does not increase the yield, its use will not be economical. In addition, similar to the conclusion of Li et al. [75], the high fertilizer-N application rate (210 kg N ha -1 ) substantially decreased the N use efficiency compared to that at lower fertilizer-N application rate (52.5 kg N ha -1 ). Therefore, fertilizer-N use efficiency should be improved by farmers' to decrease the use of high fertilizer-N rate application. Generally, NO 3 -N is the major source of soil N absorbed by crops [76] and the improvement of N recovery depend on the capture of by roots deep in the soil profile during the growing season [77]. Therefore, further research is looked-for to elucidate whether increasing N use efficiency through increasing utilization of residual soil NO 3 -N [78]. In our study, decreasing wheat yield and N use efficiency at higher fertilizer-N application rates can result in large increase in tillering and biomass production [79] and decrease the vegetative growth of organs [80], increasing lodging [81], and parasite susceptibility [82]. Numerous researchers suggested that a balanced application of fertilization can improve nutrient use efficiency and reduce environmental impacts [10,83,84], and that the application of fertilizers (N, P and K) results in higher grain yields [30,85,86]. The interaction between K and N, especially available-N and K forms on plant growth and development, has become a focus of research. Our study showed that available-N forms affect plant growth and its uptake; however, the K rate has indirectly influence on the regulation of photosynthesis and nutrient absorption, with a positive N and K interaction effects. All the N use efficiency parameters declined with increase in N rate beyond N 120 , suggesting the ideal management for higher wheat yield in this region. The increased plant dry weight and chlorophyll content is positively correlated with photosynthesis and plant growth [87]. It has been reported that application of fertilizer N in amounts more than that required to produce economic yields will lead to high N losses and low N use efficiencies [88]. The low N use efficiencies in our study suggest significant N losses or immobilization. The top dressing of fertilizer application probably resulted in much of the urea N being located on or near the soil surface, with high potential for leaching and volatilization losses of N in this slightly alkaline coarsetextured soil.
Increasing synchronization between N needed by the crop and fertilizer N supply is crucial for improving N use efficiency. Applying N when demand by the crop is high will not only increase yield but also N use efficiency [89]. Ali et al. [90] reported that fertilizer N recovery efficiency in wheat in some parts of Egypt was in the range of 35.6-51.1% by following the standard recommendation. Worldwide N recovery efficiency in cereal is reported to be~35% [2]. Improved AE and RE of applied N support the observations of Dobermann et al.
[91] who regarded AE exceeding 25 kg grain per kg applied N and RE exceeding 60% with high grain yields as efficient N management strategies for timely sown wheat. Bijay-Singh et al. [92] reported wheat response to need based fertilizer N application at MT stage. The aaccurate yield prediction requires fundamental understanding of the functional relationship between yield and these interactive factors, and to reveal such relationship requires both comprehensive datasets and powerful Algorithms Regularization, and Scaled Conjugated Gradient algorithms to train the developed ANN model for rice grain yield prediction in Sri Lanka. They reported that Levenberg-Marquardt training algorithm has outperformed the other two algorithms in determining the relationships between climatic factors and rice grain yield with less computational time. The results were stable and satisfactory under the highly unpredicted climate scenarios. ANN relationships developed can be used to predict the future rice grain yields based on climate data from various climate models. Khosla et al. [104] applied modular ANNs for predicting the amount of monsoonal rainfall and the crop yield potential of major kharif crops and reported that these machine learning approach has out-perform simulation abilities. Shastry et al. [101] compared ANNs and multiple linear regression (MLR) technique for predicting wheat grain yield based on amount of rainfall, crop biomass, soil evaporation, transpiration, soil moisture, and the amount of fertilizer-N applied to the crop. The customized ANN developed by varying the number of hidden layers and number of neurons in the hidden layer and the leaning rate had shown better performance for the prediction of wheat grain yield. Guo and Xue [34] reported high inaccuracy of the spatial neural network model in wheat yield forecasting which is limited to the forecasting of crop yield only within normal ranges. They reported that caution should be taken to use neural networks when using either Nonlinear Auto-regressive Neural Network (NARNN) and Nonlinear Autoregressive with External Input Neural Network (NARXNN) model for crop yield forecasting due to their inconsistency between the results of training and forecasting. Khaki and Wang [93] reported that deep neural network (DNN) approach had advantage of state-of-the-art modeling and solution techniques with superior prediction accuracy, with a RMSE being 12% of the average yield and 50% of the standard deviation for the validation data-set using predicted weather data. With perfect weather data, the RMSE would be reduced to 11% of the average yield and 46% of the standard deviation.

Brief description of experimental site
A 2-year field experiment (2013-14 and 2014-15) on irrigated wheat was established in 2013 starting on a Typic Ustochrept sandy loam soil at the experimental farm of the Punjab Agricultural University, Ludhiana, Punjab (30˚56 0 N and 75˚52 0 E) in the Indo Gangetic Plains (IGPs) in the north-western region of India. The surface soil (0-15 cm) layer was non-saline (electrical conductivity E.C. 1:2 = 0.24 dS m -1 ) with pH 1:2 = 7.40 (1:2 soil: water), Walkley and Black-C = 3.46 g kg -1 , available-N = 52.9 kg ha -1 ; 0.5 M NaHCO 3 -extractable P = 17.9 mg kg -1 and 1 N NH 4 OAc-extractable K = 139.8 mg kg -1 . The study region has a sub-tropical climate, with hot, wet summers and cold dry winters. Annual mean rainfall is~760 mm,~80% of which received in monsoon season extending between July and September. Mean minimum and maximum temperatures (averaged across 30 years) during wheat (November to April) are 6.7˚C and 22.6˚C and in rice (June to October) are 18˚C and 35˚C, respectively.

Experimental design and treatments
The experiment was laid out in a split plot design with three replications and consisted of six fertilizer-N application rates in main-plots and four rates of fertilizer-K rates in sub-plots. The main-plot treatments consisted of six fertilizer-N application rates of 0, 80, 120, 160, 200 and 240 kg N ha -1 (N 0 -N 240 ), and sub-plots treatments consisted of four fertilizer-K application rates of 0, 30, 60 and 90 kg Kha -1 (K 0 -K 90 ). These treatments were assigned to the same experimental plots in all the years of the study.

Fertilizer and irrigation management
Wheat crop received a different fertilizer-N (0, 80, 120,160, 200 and 240 kg N ha -1 ) and K (0, 30, 60 and 90 kg Kha -1 ) rates as urea (46% N) and muriate of potash (60% K 2 O). One-third of total fertilizer-N, and whole amount of fertilizer-P and fertilizer-K were drilled at wheat sowing each year. The remaining~2/3 rd of fertilizer-N (as per treatment) was applied in two equal split doses immediately before first irrigation at 3 weeks and second irrigation applied at 8 weeks after sowing. Wheat was irrigated (~75 mm each) at crown root initiation, maximum tillering, panicle initiation and dough stages as recommended for the crop in the region.

Soil and plant analysis and estimation of nutrients use efficiencies
Soil samples from the surface (0-15 cm) soil layer were collected after the completion of two years study period. Soil samples were dried in shade and were ground and sieved through 2 mm stainless steel sieve, and stored in plastic bottles until analysis. Soil samples were analyzed for available-N and K. The grain and straw samples collected at maturity were oven-dried at 65˚C for 48 h to a constant weight and ground to pass through a 0.5 mm screen. The total N and K contents were determined by micro-kjeldahl method and using flame photometry methods, respectively.
The partial factor productivity of K (PFP N /PFP K ), agronomic efficiency of N and K (AE N / AE N ), physiological efficiency of N and K (PE N /PE K ) and the reciprocal internal use efficiency of N (RIUE N /RIUE K ) were estimated using Eqs 9-16. The PFP was calculated as a ratio of grain yield (kg ha -1 ) and the total amount of fertilizer added (kg ha -1 ) using Eqs 9, 10. The AE was calculated a ratio of difference in grain yield (kg ha -1 ) in fertilizer-N and K added plots and the control (no-N/no-K) to the amount of fertilizer-N/fertilizer-K added (kg ha -1 ) using Eqs 11, 12. The PE was calculated as the ratio of difference in grain yield (total above-ground dry matter, kg ha -1 ) of fertilizer N/fertilizer-K applied and the control (no-N/no-K) to that of difference in total (grain + straw) N and K uptake (kg ha -1 ) from fertilizer applied and the control (Eqs 13, 14). The RIUE N of applied N and K was calculated as the ratio of N and K uptake (kg ha -1 ) by grain to the biological yield (total above-ground dry matter, Mg ha -1 ) ( Eqs 15,16).

Development of artificial neural network (ANN) model for prediction of wheat yield
The ANNs competent of learning the data-set used during the training step, and then validate and train the network with parts of the initial data set that is used during the training step [105][106][107]. The ANNs are collection of a large number of inter-connected neurons, which are helpful device to forecast the concert of a simulation system, when the availability of experimental data-set is limited [105]. The ANNs are multi-layered feed forward completely connected network consists of an input layer, one or more hidden layers and an output layer [105,108]. In the present study, we applied back propagation neural networks technique, and ANNs consisted of several layers of neurons which are inter-connected and then the weights were assigned to those inter-connections [106]. To simply clarify, weighted connections will permit to move among the layers wherein a node will accept data from the earlier layer and will compute the weighted sum for the net inputs (Eq 13).
Where, 'n'= actual number of inputs, 'w'= weight of the connection of the nodes that are 'I'and 'j', 'x'= input from 'j'and 'bi'= bias. The node outputs 'oi'was computed from the transfer function 'fi'using weighted values (Eq 14).
In back propagation neural network, input layer neurons distribute input 'X i ' to the weights 'w h ij ' of hidden layers without performing any computation. Outputs from hidden layer are computed in the first step and are passed by a following activation function (Eq 15).
Where, 'Z j ' = activationfunction, '@ j '= non-linear activation function used in a hidden layer and could be a hyperbolic tangent, sigmoid or logistic function. 'P'= input number, 'h'= symbol for hidden layer and 'γ j '= j th error term. The ANN forecasting model is formulated as Eq 16.
Where, 'ϕ' is the transfer function, 'W ji ' = weights describing connections between the 'i th'node of the input layer and the 'j th 'node of the hidden layer, 'θ j ' = biases related to the hidden layer, 'W out j ' = weights related to connection between the 'j th 'node of the hidden layer and node of the output layer and 'θ 0 ' = bias at the output layer. Therefore, to apply Eq 14 for wheat yield prediction, a suitable training algorithm was required to optimize values of 'w'and 'θ'. In the present study, ANNs provided with Levenberg-Marquardt training algorithm and hyperbolic tangent sigmoid transfer functions was used as a point of reference to examine model inputs in terms of root mean square error (RMSE), mean absolute error (MAE) and mean absolute percentage error (MAPE).
To simulate wheat grain yield (Mg ha -1 ) of the experimental data-set, ten different input layers (viz. grain N uptake, straw N uptake, grain K uptake, straw K uptake, total N uptake, total K uptake, SPAD value, green seeker value, RIUE N and RIUE K ) were used as input variables. The wheat grain yield was chosen as desired output parameter. The experimental data (pooled for two study years) were randomly divided into two sets viz. training data set (70%) and testing data set (30%).

Economic indices of wheat production
The mean cost of cash inputs (MCCIs) was estimated as sum of expenditure incurred for the purchase of inputs (US$ ha -1 ), e.g., seed, fertilizers, insecticides, fungicides, herbicides, etc. and labor cost for different field operations (Eq 17).
Mean net returns (MNR) were estimated as the difference in MGR and MCCI (Eq 19).
The benefit-cost (B-C) ratio was estimated as a ratio of MGRs and the MCCIs. The gross returns above the fertilizer cost (GRAFC) for wheat were estimated as the difference in between MGRs and amount (A) of N, P and K applied (kg ha -1 ) and price of N, P and K (US$ kg -1 ) as per treatment (Eq 20).
Where, 'A (N+P+K) 'represents amount of N+P+K applied and 'price (N+P+K) 'represents the market price of N+P+K. These estimations were based on market price of US$ 84.4 and 242.9Mg -1 for urea and MOP, respectively.
The economic efficiency was determined by dividing average net returns (ANR, US$ ha -1 ) from crop under different fertilizer treatments by crop duration (d) (Eq 21).
Economic efficiency ðUS$ ha À 1 d À 1 Þ ¼ Mean net returns ðMNRsÞ Mean crop duration ð21Þ The returns on investment (ROI) on fertilizers were estimated as a ratio of MGRs and total cost of fertilizers using Eq 22.

Statistical analysis
The data were analyzed using analysis of variance for the split plot design. All data-sets were analyzed using analysis of variance (ANOVA) and the differences between the means of treatment were separated by the least significant difference at the level of significance  (Eqs 23-26). The correspondence between the measured and predicted root biomass of rice and wheat was graphically shown using 1:1 correspondence (X = Y).
RMSE ¼ ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi P Where, 'n'= number of data points in the data set and 't'= actual output, 'z'= predicted output. The significance of regression coefficients (slope and intercept) and coefficient of determination (R 2 ) was tested using students' T and F-test, respectively.

Conclusions
Higher N fertilizer application ensured higher crop yield and N accumulation, cause potential N losses and pollute source, but was not necessary to achieve optimal crop production. However, an increase in N supply did not affect the grain yield by increased K fertilization under sufficient available-K content in illitic soils. The higher rate of N and K fertilizer application decreased nutrient use efficiencies and fertilizer productivity. It is essential to increase NUE by reducing the input of N fertilizer and increasing the N absorption of crops, and to improve the sustainability of crop production. This study would help policy makers consider artificial neural network model and economic indices of wheat production suitable for up-scaling and large-scale adoption by smallholder farmers.